I assume Wolfram Alpha is correct, but that's an assumption I'm making.

F is 15, also known as 2^4 -1.

FF is 255, also known as 2^8 -1.

These can be checked using calc in Windows and going from dec to hex.

So, sixteen F, or FFFFFFFFFFFFFFFF, should be 2^64 -1.

https://www.wolframalpha.com/input?i=convert+2%5E64+-1+to+base+36

They give 3w5e11264sgsf

mIRC 7.69

//echo $base(FFFFFFFFFFFFFFFF,16,36)

3W5E11264SG0G

mIRC 6.03

//echo $base(FFFFFFFFFFFFFFFF,16,36)

3W5E11264SGSF

So, did newer versions of mIRC start miscalculating using $base or is Wolfram Alpha incorrect? Or possibly both incorrect?

Did a search and came across https://books.google.com/books?id=qDszEAAAQBAJ&pg=PT237&lpg=PT237&dq="3W5E11264SGSF"

Maybe they made a mistake there, but, maybe someone else here can verify what base 16 FFFFFFFFFFFFFFFF should be in base 36. I suspect newer versions of mIRC have a math bug in $base.

Edited...

More things I found out playing around.

//inc %n 1 | tokenize 32 $calc(20000000000000 + %n) | echo -s $base($1-,16,36)

In 7.69

Done seven times

2GOSA7PA2GW

2GOSA7PA2GY

2GOSA7PA2H0

2GOSA7PA2H0

2GOSA7PA2H0

2GOSA7PA2H2

2GOSA7PA2H4

In 6.03

2GOSA7PA2GX

2GOSA7PA2GY

2GOSA7PA2GZ

2GOSA7PA2H0

2GOSA7PA2H1

2GOSA7PA2H2

2GOSA7PA2H3

In 7.69

//echo -s $base(2GOSA7PA2H0,36,16)

//echo -s $base(2GOSA7PA2H1,36,16)

Same result of 20000000000004

In 6.03

//echo -s $base(2GOSA7PA2H0,36,16)

20000000000004

//echo -s $base(2GOSA7PA2H1,36,16)

20000000000005

Wolfram Alpha

https://www.wolframalpha.com/input?i=convert+2GOSA7PA2H1_36+to+base+1620000000000005_16

So, Wolfram Alpha takes 2GOSA7PA2H1 in base 36 and converts it to 20000000000005 in base 16.